Problem: If $x \circledcirc y = 7x+y$ and $x \barwedge y = 8x-3y$, find $-6 \circledcirc (5 \barwedge -5)$.
Solution: First, find $5 \barwedge -5$ $ 5 \barwedge -5 = (8)(5)-(3)(-5)$ $ \hphantom{5 \barwedge -5} = 55$ Now, find $-6 \circledcirc 55$ $ -6 \circledcirc 55 = (7)(-6)+55$ $ \hphantom{-6 \circledcirc 55} = 13$.